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Maths

Department Vision:

Mathematics contributes to the school curriculum by developing pupils’ abilities to calculate; to reason logically, algebraically, and geometrically; to solve problems and to handle data. Mathematics is important for pupils in many other areas of study, particularly Science and Technology. It is also important in everyday living and in many forms of employment.

As a department we will set targets and have high expectations for all our students. The department will offer a variety of approaches to teaching and learning to keep the pupils engaged, motivated and therefore enhances their enjoyment of Mathematics. Please follow the maths department twitter page: @SFXmaths

Curriculum Information

Key Stage 3

Year 7

Term 1 Topics & Content:

Numbers and the Number System: Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor and lowest common multiple. Use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5. Recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions.

Counting and comparing: order positive and negative integers, decimals and fractions. Use the symbols =, ≠, <, >, ≤, ≥

Calculating: understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals). Apply the four operations, including formal written methods, to integers and decimals. Use conventional notation for priority of operations, including brackets. Recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions).

Visualising and Constructing: use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries. Use the standard conventions for labelling and referring to the sides and angles of triangles. Draw diagrams from written description

Investigating Properties of Shape: identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres. Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language.

Term 2 Topics & Content:

Algebraic Proficiency: Tinkering: Understand and use the concepts and vocabulary of expressions, equations, formulae and terms. Use and interpret algebraic notation, including: ab in place of a × b, 3y in place of y + y + y and 3 × y, a² in place of a × a, a³ in place of a × a × a, a/b in place of a ÷ b, brackets. Simplify and manipulate algebraic expressions by collecting like terms and multiplying a single term over a bracket. Where appropriate, interpret simple expressions as functions with inputs and outputs. Substitute numerical values into formulae and expressions. Use conventional notation for priority of operations, including brackets.

Exploring Fractions, Decimals and Percentages: Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1. Define percentage as ‘number of parts per hundred’. Express one quantity as a percentage of another

Proportional Reasoning: Use ratio notation, including reduction to simplest form. Divide a given quantity into two parts in a given part: part or part: whole ratio

Pattern Sniffing: Generate terms of a sequence from a term-to-term rule.

Investigating Angles: Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles. Calculating Fractions, Decimals and Percentages: Apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers. Interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively. Compare two quantities using percentages. Solve problems involving percentage change, including percentage increase/decrease

Term 3 Topics & Content:

Solving Equations and Inequalities: Recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions). Solve linear equations in one unknown algebraically.

Calculating Space: Use standard units of measure and related concepts (length, area, volume/capacity). Calculate perimeters of 2D shapes. Know and apply formulae to calculate area of triangles, parallelograms, trapezia. Calculate surface area of cuboids. Know and apply formulae to calculate volume of cuboids. Understand and use standard mathematical formulae.

Checking, Approximating and Estimating: Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures). Estimate answers; check calculations using approximation and estimation, including answers obtained using technology. Recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)

Mathematical Movement: Work with coordinates in all four quadrants. Understand and use lines parallel to the axes, y = x and y = -x. Solve geometrical problems on coordinate axes. Identify, describe and construct congruent shapes including on coordinate axes, by considering rotation, reflection and translation. Describe translations as 2D vectors

Numbers and the Number System: Use the concepts and vocabulary of prime numbers, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem. Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures). Interpret standard form A × 10n, where 1 ≤ A < 10 and n is an integer.

Calculating: Apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative. Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals.

Visualising and Constructing: Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings. Identify, describe and construct similar shapes, including on coordinate axes, by considering enlargement. Interpret plans and elevations of 3D shapes. Use scale factors, scale diagrams and maps

Understanding Risk: Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale. Record, describe and analyse the frequency of outcomes of probability experiments using tables. Construct theoretical possibility spaces for single experiments with equally likely outcomes and use these to calculate theoretical probabilities. Apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one.

Algebraic Proficiency – Tinkering: Use and interpret algebraic notation, including: a²b in place of a × a × b, coefficients written as fractions rather than as decimals. Understand and use the concepts and vocabulary of factors. Simplify and manipulate algebraic expressions by taking out common factors and simplifying expressions involving sums, products and powers, including the laws of indices. Substitute numerical values into scientific formulae. Rearrange formulae to change the subject.

Term 2 Topics & Content:

Exploring Fractions, Decimals and Percentages: Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8).

Proportional Reasoning: Express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations). Identify and work with fractions in ratio problems. Understand and use proportion as equality of ratios. Express a multiplicative relationship between two quantities as a ratio or a fraction. Use compound units (such as speed, rates of pay, unit pricing). Change freely between compound units (e.g. speed, rates of pay, prices) in numerical contexts. Relate ratios to fractions and to linear functions.

Pattern Sniffing: Generate terms of a sequence from either a term-to-term or a position-to-term rule. Deduce expressions to calculate the nth term of linear sequences.

Investigating Angles: Understand and use alternate and corresponding angles on parallel lines. Derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons).

Calculating Fractions, Decimals and Percentages: Interpret fractions and percentages as operators. Work with percentages greater than 100%. Solve problems involving percentage change, including original value problems, and simple interest including in financial mathematics. Calculate exactly with fractions.

Solving Equations and Inequalities: Solve linear equations with the unknown on both sides of the equation. Find approximate solutions to linear equations using a graph.

Measuring Data: Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers). Apply statistics to describe a population.

Year 9

Term 1 Topics & Content:

Calculating: Calculate with roots, and with integer indices. Calculate with standard form A × 10n, where 1 ≤ A < 10 and n is an integer. Use inequality notation to specify simple error intervals due to truncation or rounding. Apply and interpret limits of accuracy.

Visualising and Constructing: Use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle). Use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line. Construct plans and elevations of 3D shapes.

Algebraic Proficiency – Tinkering: Understand and use the concepts and vocabulary of identities. Know the difference between an equation and an identity. Simplify and manipulate algebraic expressions by expanding products of two binomials and factorising quadratic expressions of the form x² + bx + c. Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments. Translate simple situations or procedures into algebraic expressions or formulae.

Proportional Reasoning: Solve problems involving direct and inverse proportion including graphical and algebraic representations. Apply the concepts of congruence and similarity, including the relationships between lengths in similar figures. Change freely between compound units (e.g. density, pressure) in numerical and algebraic contexts. Use compound units such as density and pressure.

Solving Equations and Inequalities I: Understand and use the concepts and vocabulary of inequalities. Solve linear inequalities in one variable. Represent the solution set to an inequality on a number line.

Conjecturing: Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS). Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs.

Term 3 Topics & Content:

Algebraic Proficiency – Visualising: Identify and interpret gradients and intercepts of linear functions algebraically. Use the form y = mx + c to identify parallel lines. Find the equation of the line through two given points, or through one point with a given gradient. Interpret the gradient of a straight line graph as a rate of change. Recognise, sketch and interpret graphs of quadratic functions. Recognise, sketch and interpret graphs of simple cubic functions and the reciprocal function y = 1/x with x ≠ 0. Plot and interpret graphs (including reciprocal graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration.

Solving Equations and Inequalities II: Solve, in simple cases, two linear simultaneous equations in two variables algebraically. Derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution. Find approximate solutions to simultaneous equations using a graph.

Presentation of Data: Interpret and construct tables, charts and diagrams, including tables and line graphs for time series data and know their appropriate use. Draw estimated lines of best fit; make predictions. Know that correlation does not indicate causation; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

Calculating: Estimate powers and roots of any given positive number Calculate with roots, and with integer and fractional indices. Calculate exactly with surds. Apply and interpret limits of accuracy, including upper and lower bounds.

Mathematical movement I: Identify, describe and construct similar shapes, including on coordinate axes, by considering enlargement (including fractional scale factors). Make links between similarity and scale factors. Describe the changes and invariance achieved by combinations of rotations, reflections and translations.

Algebraic Proficiency – Tinkering: Simplify and manipulate algebraic expressions involving algebraic fractions. Manipulate algebraic expressions by expanding products of more than two binomials. Simplify and manipulate algebraic expressions (including those involving surds) by expanding products of two binomials and factorising quadratic expressions of the form x² + bx + c, including the difference of two squares. Manipulate algebraic expressions by factorising quadratic expressions of the form ax² + bx + c.

Term 2 Topics & Content:

Proportional Reasoning: Interpret equations that describe direct and inverse proportion. Recognise and interpret graphs that illustrate direct and inverse proportion. Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y.

Pattern Sniffing: Deduce expressions to calculate the nth term of quadratic sequences. Recognise and use simple geometric progressions (r^n where n is an integer, and r is a rational number > 0).

Solving Equations and Inequalities II: Solve linear inequalities in two variables. Represent the solution set to an inequality using set notation and on a graph.

Calculating Space: Calculate surface area and volume of spheres, pyramids, cones and composite solids. Apply the concepts of congruence and similarity, including the relationships between length, areas and volumes in similar figures.

Conjecturing: Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results.

Term 3 Topics & Content:

Algebraic Proficiency – Visualising I: Plot and interpret graphs (including exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration. Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts. Interpret the gradient at a point on a curve as the instantaneous rate of change. Identify and interpret roots, intercepts, turning points of quadratic functions graphically.

Exploring Fractions, Decimals and Percentages: Change recurring decimals into their corresponding fractions and vice versa. Set up, solve and interpret the answers in growth and decay problems, including compound interest.

Algebraic Proficiency – Visualising II: Use the form y = mx + c to identify perpendicular lines. Recognise and use the equation of a circle with centre at the origin. Find the equation of a tangent to a circle at a given point

Mathematical movement II: Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors.